Logic system for DPA resistance and/or side channel attack resistance

ABSTRACT

DPA-resistant logic circuits and routing are described. An architecture and methodology are suitable for integration in a common automated EDA design tool flow. The architecture and design methodology can be used in logic circuits, gate arrays, FPGAs, cryptographic processors, etc. In one embodiment, the implementation details of how to create a secure encryption module can be hidden from the designer. The designer is thus, able to write the code for the design of DPA-resistant logic circuits using the same design techniques used for conventional logic circuits. Contrary to other complicated DPA -blocking techniques, the designer does not need specialized knowledge and understanding of the methodology. In one embodiment, the automated design flow generates a secure design from a Verilog or VHDL netlist. The resulting encryption module has a relatively constant power consumption that does not depend on the input signals and is thus relatively independent of which logic operations are performed.

REFERENCE TO RELATED APPLICATIONS

The present application claims priority benefit of U.S. ProvisionalApplication No. 60/544,809, filed Feb. 13, 2004, titled “LOGIC SYSTEMFOR DPA RESISTANCE”, and U.S. Provisional Application No. 60/613,059,filed Sep. 24, 2004, titled “MULTIPLE DIFFERENTIAL PAIR ROUTING”, theentire contents of both provisional applications are hereby incorporatedby reference.

U.S. GOVERNMENT INTEREST STATEMENT

Portions of the disclosed invention were made under contract with anagency of the United States Government under NSF, Government ContractNo. CCR-0098361. The U.S. Government has certain rights in portions ofthe invention.

BACKGROUND

1. Field of the Invention

The present invention relates to logic systems that are resistant todifferential power analysis and other side channel attacks (SCA).

2. Description of the Related Art

When encryption algorithms are implemented on a physical device, thedevice itself often provides an attacker with important sidechannel-information to obtain the secret key. For example, DifferentialPower Analysis (DPA) uses the fact that logic operations have powercharacteristics that depend on the input data.

DPA has been used against Smart Cards, where the security IC is ofteneasily observable. Smart Cards are used in a broad range ofapplications. The four main sectors are (1) Telecommunications, e.g. SIMcards in GSM mobile phones; (2) Financial Services, e.g. electronicwallets, ATM and credit cards; (3) Pay TV; and (4)Government/Healthcare, e.g. secure ID cards containing biometricinformation.

Many countermeasures have been proposed to try and conceal the supplycurrent variations at the architectural or the algorithmic level. Yet,the proposed countermeasures are not effective or practical against DPAand/or its derivatives, as the variations actually originate at thelogic level.

SUMMARY

These and other problems are solved by providing DPA-resistant logiccircuits. An architecture and methodology are suitable for integrationin a common automated EDA design tool flow. The architecture and designmethodology can be used in logic circuits, gate arrays, FPGAs,cryptographic processors, etc.

In one embodiment, the implementation details of how to create a secureencryption module can be hidden from the designer. The designer is thus,able to write the code for the design of DPA-resistant logic circuitsusing the same design techniques used for conventional logic circuits.Contrary to other complicated DPA-blocking techniques, the designer doesnot need specialized knowledge and understanding of the methodology. Inone embodiment, the automated design flow generates a secure design froma Verilog or VHDL netlist. The resulting encryption module has arelatively constant power consumption that does not depend on the inputsignals and is thus relatively independent of which logic operations areperformed. In one embodiment, the present design methodology usesexisting resources and as a result can be readily applied. In oneembodiment, the architecture and design methodology blocks DPA at thelogic level, freeing the designer to concentrate on preventing otherside channels at a different level of abstraction (e.g., conditionalbranching with unequal lengths, etc.)

In one embodiment, a Simple Dynamic Differential Logic (SDDL) isprovided, wherein a differential logic stage includes pre-charge orpre-discharge circuits to prevent DPA and SCA. In one embodiment, a WaveDynamic Differential Logic (WDDL) is provided, wherein a differentiallogic stage is pre-charged or pre-discharged by a previous logic stage,such as, for example, a previous SDDL stage, a WDDL stage, etc. In oneembodiment, a Divided Wave Dynamic Differential Logic (DWDDL) isprovided wherein a WDDL circuit is conveniently implemented as duallogic trees.

In one embodiment, a Dynamic and Differential Logic is provided withoutthe disadvantages of (1) having a large load on the pre-charge controlsignal and (2) low noise margins. In one embodiment, a charge is notstored on a high-impedance node. In one embodiment, static CMOS gateshave their output connected to either VDD or GND.

In one embodiment, EDA tools are used to route multiple differentialpairs. In one embodiment, each output pair is routed as a “fat” wire,which has among other characteristics the width of two parallel wiresplus spacing. Afterwards, the fat wires are split into the twodifferential lines.

One embodiment includes a method for differential pair conductor routingin a logic circuit, by routing conductors of a first line width toobtain vertical conductors of the first line width, horizontalconductors of the first line width, and vias to connect the verticalconductors and the horizontal conductors, separating at least one of thevertical conductors of the first line width into parallel first andsecond differential vertical conductors of a second line width, wherethe second line width is smaller than one-half of the first line width,separating at least one of the horizontal conductors of the first linewidth into parallel first and second differential horizontal conductorsof the second line width, and separating a via connecting the at leastone of the vertical conductors to the at least one of the horizontalconductors into first and second vias; the first via connecting thefirst differential vertical conductor to the first differentialhorizontal conductor and the second via connecting the seconddifferential vertical conductor to the second differential horizontalconductor. In one embodiment, the first and second vias and/or wireshave a substantially equal width. In one embodiment, the first andsecond vias and/or wires have different widths.

In one embodiment, the method includes replacing conventional logic usedfor the routing with differential logic. In one embodiment, the methodincludes doubling a grid pitch. In one embodiment, a centerline of aspace between the parallel first and second differential horizontalconductors corresponds to a centerline of the at least one horizontalconductor.

In one embodiment, the routing is provided by an automated softwarerouting tool. In one embodiment, the routing is provided by usingSilicon Ensemble from Cadence Software, Inc.

One embodiment includes a method for differential pair conductor routingin a logic circuit, by routing conductors of a first line width toobtain a first routing for a first logic library, wherein vertical andhorizontal paths are separated such that vertical and horizontalconductors do not short, wherein connections between the vertical andhorizontal paths are provided by vias, separating conductor paths in thefirst routing into differential paths by splitting the conductors of afirst line width into spaced parallel conductors of a second line width,where the second line width is smaller than the first line width,separating the vias into pairs of vias, and replacing the first logiclibrary with a differential logic library. In one embodiment, the firstand second vias and/or wires have a substantially equal line width. Inone embodiment, the first and second vias and/or wires have differentline widths.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 shows one embodiment of a Simple DDL (SDDL) 2-input AND gate.

FIG. 2 shows embodiments of an SDDL precharge and predischarge operator.

FIG. 3 shows one embodiment of an SDDL register.

FIG. 4 shows one embodiment of an SDDL register.

FIG. 5 shows that both signals of the differential output have aswitching event, even though the differential inputs each have only oneswitching event.

FIG. 6 shows the 2-input SDDL AND-gate, the truth table of the SDDLAND-gate, and the final 2-input WDDL AND-gate implementation.

FIG. 7 shows the Master-Slave WDDL register.

FIG. 8 shows one embodiment of a WDDL implementation of a combinatoriallogic tree.

FIG. 9 shows that the output Z of the example circuit has 2 switchingevents even though the inputs A and B both have only one switchingevent.

FIG. 10 shows an alternate logic system to provide the true and thefalse input at the original single-ended combinatorial logic.

FIG. 11 shows one embodiment of a design flow for DPA-resistant logic.

FIG. 12A shows an example single-ended logic function.

FIG. 12B shows one embodiment of the logic function of FIG. 12Aimplemented as WDDL logic.

FIG. 13A shows the “fat” wires.

FIG. 13B shows the translation from “fat” wires to differential wires.

FIG. 13C shows the resulting differential wires.

FIG. 14 shows a differential routing methodology.

FIG. 15A shows capacitive coupling between differential pairs.

FIG. 15B shows reduced capacitive coupling between differential pairs byusing power or ground lines as shielding.

FIG. 15C shows reduced capacitive coupling between differential pairs byincreasing separation between the pairs.

DESCRIPTION

In one embodiment, a logic-level DPA-resistant architecture and designmethodology is provided using standard building blocks to make a new‘compound’ library.

Various embodiments of Dynamic and Differential Logic (DDL) are used. ADifferential Logic style provides one or more pairs of output signalswith opposite logic polarity (e.g., an inverted output and acorresponding non-inverted output of the same logic variable), which forconvenience are herein referred to as the true signal and the falsesignal. In addition to a differential output, the input signals aredifferential too. In one embodiment, the Dynamic Logic style alternatespre-charge and evaluation phase, in which the output is pre-(dis)charged and conditionally evaluated respectively.

FIG. 1 shows one embodiment of a Simple DDL (SDDL) 2-input AND gate 100.In the SDDL AND gate 100, inputs A and B are provided to an AND gate102, and inverted inputs A and B are provided to an OR gate 103. Anoutput of the AND gate 102 is provided to a first input of an AND gate104, and an output of the OR gate 103 is provided to a first input of aNAND gate 105. An inverted precharge input prch is provided torespective second inputs of the AND gate 104 and the NAND gate 105.(Note, for convenience, in the present disclosure, an underscore is usedto denote inversion rather than the more conventional overscore.) Anoutput of the AND gate 104 corresponds to an uninverted (normal) outputof the gate 100 and an output of the NAND gate 105 corresponds to aninverted output of the gate 100.

Creating a compound standard cell, which has a dynamic differentialbehavior, is done with the help of: (1) the De-Morgan's Law, whichallows expressing the false output of any logic function, using thefalse inputs of the original logic function; and (2) AND-ing thedifferential output with a pre-charge signal. Because of the AND-ingwith the pre-charge signal, whenever the pre-charge signal is “1”, theinverted prch signal is “0” as shown in FIG. 1 and the outputs arepre-discharged to “0” independently of the input-values. On the otherhand, whenever the pre-charge signal is “0”, exactly one output, whichis specified by the inputs, will evaluate to “1”. For example, FIG. 1shows one embodiment of a Simple DDL (SDDL) 2-input AND-gate 100. Thismethodology can be applied to standard logic functions such as, forexample, OR, AND, NOR, NAND, XOR, and the like in a logic cell or FGPAslice, etc. FIG. 1 shows a SDDL AND gate with pre-‘dis’-charge logicwhere the outputs are pre-discharged to zero by AND-ing the outputs withthe inverted prch signal.

FIG. 2 shows various embodiments 201-205 of applying the prechargesignal prch in SDDL logic gates. In a first embodiment 201, an input inis provided to a first input of a first AND gate and an inverted inputin is provided a first input of a second AND gate. The signal prch isprovided to respective second inputs of the first and second AND gates.The first AND gate provides an output out, and the second AND gateprovides an inverted output out. One of ordinary skill in the art willrecognize that the precharge/predischarge operation can be implementedin many ways, and the embodiments in the figures are not intended to belimiting.

In a second embodiment 202, an input in is provided to a first input ofa first NOR gate and an inverted input in is provided a first input of asecond NOR gate. The signal prch is provided to respective second inputsof the first and second NOR gates. The second NOR gate provides anoutput out, and the first NOR gate provides an inverted output out.

In a third embodiment 203, an input in is provided to a first input of afirst OR gate and an inverted input in is provided a first input of asecond OR gate. The signal prch is provided to respective second inputsof the first and second OR gates. The first OR gate provides an outputout, and the second OR gate provides an inverted output out.

In a fourth embodiment 204, an input in is provided to a first input ofa first NAND gate and an inverted input in is provided a first input ofa second NAND gate. The signal prch is provided to respective secondinputs of the first and second NOR gates. The second NAND gate providesan output out, and the first NAND gate provides an inverted output out.

A fifth embodiment 205 shows the embodiment 202 where a single-endedinput is converted to a double-ended input by using an inverter. One ofordinary skill in the art will recognize that this technique forgenerating a double-ended input can also be used in connection with theembodiments 201, 203 and 204, as well as other embodiments.

As shown in FIG. 2, building pre-charge logic, which is logic thatpre-charges the outputs to ‘1’, can be done by OR-ing the differentialoutputs obtained after application of the De-Morgan's law with apre-charge signal. FIG. 2 (203) shows one embodiment of the OR-ingoperation. Static Complementary CMOS logic is inverting logic. As aresult, for an ASIC implementation of the SDDL, it is typically usefulin terms of area and power consumption to implement the pre-dischargeoperation as shown in FIG. 2 (202) and the pre-charge operation as shownin FIG. 2 (204).

An SDDL gate can be constructed from any logic function ƒ(x,y,z) byconstructing a dual logic function ƒbar(xbar,ybar,zbar) which calculatesthe inverse of ƒ(x,y,z) with xbar, ybar and zbar being the inverse ofx,y,z respectively. This can be done many ways, one of which is to useDe-Morgan's Law to writeFbar(xbar,ybar,zbar)=inv(ƒ(inv(xbar),inv(ybar),inv(zbar)), where inv()is a logical inversion. A precharge operator/function is attached at theoutputs of ƒ and ƒbar which precharges the outputs with a prechargesignal. Example embodiments 201-204 of the precharge operators are shownin FIG. 2. Additionally, to further reduced power signature, thecells/functions can be placed close to each other to equalize the loadcapacitance. The SDDL can be constructed in a FPGA and standard cells.

FIG. 3 shows one embodiment of an SDDL register 300. In the register300, an input signal in is provided to a first Flip/Flop (FF) 301, andin is provided to an input of a second FF 302. A clock signal clk isprovided to the FF 301 and the FF 302. An output of the FF 301 isprovided to a first input of a NOR gate 303, and an output of the FF 302is provided to a first input of a NOR gate 304. The clk signal isprovided to respective second inputs of the NOR gates 303, 304. Anoutput of the NOR gate 304 is an uninverted output out of the register300, and an output of the NOR gate 303 is an inverted output out of theregister 300. As shown in a waveform 310, the clk signal is logic-lowduring an evaluation phase and logic-high during a precharge phase.

Aside from building logic functions, it is desirable to be able to storea value in a storage register (e.g., a flip-flop memory cell, etc.).FIG. 3 shows a first implementation of an SDDL register 300. One pair offlip-flops in parallel stores the values of the differential true andfalse inputs. The flip-flops are clocked by the same clock (or bysynchronized clocks).

FIG. 4 shows one embodiment of a master-slave SDDL memory 400, having amaster register 401 and a slave register 402. The registers 401 and 402are similar to the register 300 shown in FIG. 3 with the NOR gates 302,303 replaced by AND gates. In the master register 401, where a prechargesignal prch is provided to the respective second inputs of the AND gatesinstead of the clk signal. The inverted and non-inverted outputs of themaster register 401 are provided to the respective inverted andnon-inverted inputs of the slave register 402. In the master register401, precharge signal prch is provided to the respective second inputsof the AND gates. In the slave register 402, the inverted prechargesignal prch is provided to the respective second inputs of the ANDgates. As shown in a timing diagram 410, the clock signal clk operatesat twice the frequency of the precharge signal prch. During a firstclock cycle, the precharge signal is held at logic low, during a secondclock cycle, the precharge signal is held at a logic high.

The register design of FIG. 4 is based on a master-slave concept. Twoflip-flop pairs in series store the values of the differential true andfalse input. The flip -flops are clocked with the same clock. Eachflip-flop samples and stores its input at the rising clock edge. Themaster 401, which is the first parallel flip-flop pair, is pre-chargedwith the inverted pre-charge signal. The slave 402, which is the secondparallel flip-flop pair, is pre -charged with the pre-charge signal. Thepre-charge signal is at half the clock frequency.

One of ordinary skill in the art will recognize that theprecharge/predischarge operation can be implemented in many ways, andthe embodiments in the figures are not intended to be limiting. Forexample, in one embodiment, the precharge operation can be provided byinterchanging the NOR gates of FIG. 3 with the AND gates of FIG. 2 (201)(e.g., by generating pre-charge logic of FIG. 2 (203, 204) instead ofpre-discharge logic of FIG. 2 (201, 202). Other examples can be givenfor FIG. 4, such as, for example, by removing the precharge operator inthe slave (which is the last flip-flop pair).

One advantage of the implementation in FIG. 4 is that on each cycle allflip-flops and their internal nodes are reset. As a consequence, onevery cycle the same event happens in the SDDL compound register. Ascompared to FIG. 3, the implementation of FIG. 4 at higher clockfrequency for the same throughput has higher power consumption, largerarea and larger clock load. Special design rules, like NP-rules ordomino logic rules, are not necessary when cascading the gates in orderto build combinatorial logic. Compound standard cells can beinterconnected. However, there is typically no guarantee that eachcompound gate has only one switching event per cycle. This is easilyseen with an example as shown in FIG. 5.

FIG. 5 shows that both signals of the differential output of a gate 500have a switching event, even though the differential inputs each haveonly one switching event. In FIG. 5, inputs A and B are provided to anexclusive-or (XOR) gate 501 and inverted inputs A and B are provided toinputs of an exclusive-nor (XNOR) gate 502. An output of the gate 501 isprovided to a first input of an AND gate 503, and an output of the gate502 is provided to a first input of an AND gate 504. The invertedprecharge signal prch is provided to respective second inputs of the ANDgates 503, 504. The output of the AND gate 503 is an output Z and theoutput of the AND gate 504 is an output Z.

The timing diagram of FIG. 5 shows that both signals of the differentialoutput have a switching event, even though the differential inputs eachhave only one switching event. Note that both the timing and the valuesof the inputs will influence the number of switching events. In a largecircuit, the glitches propagate to other gates and the number ofswitching events is undefined, as is the power consumption.

One of ordinary skill in the art will recognize that vulnerability toDPA attacks is reduced by designing logic having a switching factorrelatively close to 100%, as described herein, wherein during each cyclea relatively constant capacitance is charged or discharged.

Wave Dynamic Differential Logic (WDDL)

Any logic function in Boolean algebra can be expressed with only threeoperators, namely, the “invert”, “AND” and “OR” operators. The OR andAND operators are dual operators: applying DeMorgan's law on oneoperator will result in the other operator. An inverter is redundant indifferential logic because differential logic has both the true and thefalse output. Thus there is no need for an inverter, as inversion issimply implemented by exchanging the outputs. Restricting the problem tothe conception of a secure version of the AND- and OR-operator hasseveral advantages.

FIG. 6 shows the 2-input SDDL AND-gate 100, the truth table of the SDDLAND-gate 610, and the final 2-input WDDL AND gate 600.

The differential input signals, which are the outputs of precedingdynamic gates, pre-charge to ‘0’. As a result, whenever the inputs of anany-input AND-gate or an any-input OR-gate are pre-charged to ‘0’, theoutput signals are automatically at ‘0’. There is no need to force theoutput signals to ‘0’. Consequently, performing the predischargeoperation inside the SDDL any-input AND-gate and the SDDL any-inputOR-gate is redundant and can be omitted. As an example, FIG. 6 shows thetruth table 610 of the 2-input SDDL AND-gate 100. The table shows thatwhenever the input signals are predischarged to ‘0’, the differentialoutput signals are at ‘0’. FIG. 6 also shows the final 2-input WDDLAND-gate 600. This methodology can be applied to all any-input AND- andOR-gates of a standard cell library or within a slice on an FPGA.Although described above in terms of a pre-discharge, one of ordinaryskill in the art will recognize that the system can also be configuredto precharge to 1 and transmit the precharge 1 to the next gate.

In WDDL, the function ƒ (described above in connection with SDDL) isconstructed using non-inverting dual operators, such as, for example,AND and OR operators. Additionally, the input signals can be inverted(as, for example, in an XOR gate) and/or the output signals can beinverted. This allows the gate to pass on the precharge wave to the nextgate. Since each gate passes on the precharge wave. The prechargeoperators at ƒ and ƒbar can be omitted. The precharge wave can begenerated at the inputs and propagate by master slave flipflops withoutprecharge (or master slave flipflops with precharge), or at the inputsand at each flip-flop by using the flipflop 300.

Special design rules, like NP-rules or domino logic rules, are notnecessary when cascading the gates in order to build combinatoriallogic. Compound standard cells can be interconnected. It can be shown,that every compound WDDL gate in the combinatorial logic tree has only 1switching event per cycle. The pre-charged ‘0’s will ripple through thecombinatorial logic. In other words, instead of a pre-charge signal thatresets the logic, there is a pre-charge wave: hence the name WaveDynamic Differential Logic (WDDL). WDDL provides a Dynamic andDifferential Logic without the disadvantage of having a large load onthe pre-charge control signal. The gates are pre-charged withoutdistributing the pre-charge signal to each individual gate.

There are various ways to launch the pre-charge wave. The first methodis to insert the pre-charge operator at the beginning of everycombinatorial logic tree, i.e., at all inputs of the encryption moduleand at the outputs of all registers, as is automatically done by usingthe registers presented in FIG. 3 and FIG. 4. The second method is shownin FIG. 7. FIG. 7 shows a pre-charge operator 701 that launches apre-charge wave to a WDDL logic block 700.

It is sufficient to pre-charge the input signals of the completeencryption module such that they alternate between pre-charged zeros andactual logic values. A prerequisite is that Master-Slave WDDL registersare used. The Master-Slave WDDL register, which is depicted as FF inFIG. 7, is the SDDL register presented in FIG. 4 without the pre-chargeoperation. Once the pre-charged signals have propagated, the encryptionmodule is in stable operation mode. From then on, the registers willlaunch the pre-charge wave since they store the pre-charged zeros,sampled at the end of the preceding pre-charge phase, during theevaluation phase. Feedback and/or feedforward can be provided in thepipeline, the input signals and the combinatorial logic concurrentlyinterleave pre-charge mode and evaluation mode.

Divided Wave Dynamic Differential Logic (DWDDL)

FIG. 8 shows one embodiment of a WDDL implementation 801 of acombinatorial logic tree. When an inversion is not present in theoriginal single-ended combinatorial logic tree, the WDDL tree can beimplemented as two logic trees 802, as shown in FIG. 8. These two logictrees 802 are dual, which means that one logic tree can be derived fromthe other by inverting the inputs and by replacing the single endedAND-gates by single ended OR-gates and the single ended OR-gates bysingle ended AND-gates, etc. One logic tree generates the true outputswhile the other logic tree the false outputs.

In one embodiment shown in FIG. 8, it is possible to place and route theoriginal gate level netlist and subsequently take this layout andinterchange the AND- and OR-gates in order to make the dual logic tree.The combination of the two single ended combinatorial logic trees,called a Divided Wave Dynamic Differential Logic (DWDDL), has the samebehavior as the original WDDL.

This approach is convenient in that inside the combinatorial logic treeinterconnects can be routed in the same environment. The true and thefalse signal both see the ‘same’ environment even though they arephysically not routed in the same environment. A further advantage isthat the step of generating compound standard cells of the logic gatesis avoided. It is still desirable to match the interconnects of theinputs to the combinatorial logic tree and to generate compound standardcells for the registers. In DWDDL, inversions inside a combinatoriallogic tree are an issue. The inversion halts the pre-charge wave: the‘0’ at the input of the inverter is propagated as a ‘1’ at the output ofthe inverter, One solution is to leave the inversion in thecombinatorial logic but to insert a pre-charge operation after theinverter. This approach however, has a switching factor higher than100%. This is shown by an example in FIG. 9.

FIG. 9 shows that the output Z of the example circuit 900 has twoswitching events even though the inputs A and B both have only oneswitching event. In FIG. 9, an input A of an “original” layout 900 isprovided to an input of an inverter 901. An output of the inverter 901is provided to a first input of an AND gate 902. The inverted prechargesignal prch is provide to a second input of the AND gate 902. An outputof the AND gate 902 is provided to a first input of an OR gate 903 andthe B input is provided to a second input of the OR gate 903. An outputof the OR gate 903 is a signal Z.

FIG. 9 also shows a dual layout 910. The dual layout 910 is a dual ofthe “original” layout 900. In the dual layout 910, the input A of the“original” layout 900 is provided to an input of an inverter 911. Anoutput of the inverter 911 is provided to a first input of an AND gate912. The precharge signal prch is provided to a second input of the ANDgate 912. An output of the AND gate 912 is provided to a first input ofan AND gate 913 and the B input is provided to a second input of the ANDgate 913. An output of the AND gate 913 is the signal Z.

The timing diagram of FIG. 9 shows that the output Z of the examplecircuit has two switching events, even though the inputs A and B bothhave only one switching event. Note that both the timing and the valuesof the A and B inputs will influence the number of switching events. Ina large circuit, the glitches propagate to other gates and the number ofswitching events is undefined.

FIG. 10 shows an alternate solution to the inversion issue in a system1000 to provide the true and the false input at the originalsingle-ended combinatorial logic. In the system 1000, normal(uninverted) and inverted inputs are provided to an AND/OR logic block1001 and to a complementary OR/AND logic block 1002. The logic block1001 provides an uninverted output and the complementary logic block1002 provides an inverted output. In the system 1000, the combinatoriallogic can be implemented without further inversions. The single-endedcombinatorial logic tree can be synthesized and optimized as multilevellogic. It can also be implemented as a Programmable Logic Array. NOR-NORPLAs and NAND-NAND PLAs can be used. These implementations have aswitching factor of 100% despite the inversions.

FIG. 11 shows an embodiment of a design flow 1100 that begins with adesign specification 1101. The design specification 1101 is provided toa logic design and verification operation 1102. Data from the logicdesign and verification operation 1102 and data from a standard celllibrary 1110 are provided to a logic synthesis module 1103. Logiccircuits from the logic synthesis module 1103 are provided to a placeand route module 1105. The place and route module 1105 produces aphysical layout specification 1106.

FIG. 11 shows one embodiment of a design flow. In synchronous logic, thelogic design of a module can be done with a standard hardwaredescription language, such as Verilog or VHDL. Synthesis is done using asubset of a regular static CMOS standard cell library 1110. The subsetincludes the inverter, AND-gate, OR-gate and a register. A more extendedlibrary can also be used both for ASIC and FPGA . Subsequently, script1104, e.g., in PERL or AWK, transforms the resulting synthesized code atgate level to a code that reflects the differential gates. The script1104 replaces the single ended gates with the differential dynamicgates, removes the inverters and establishes the right connections. Nextthe single ended gates are put together to form the compound standardcells. Then these cells can be placed by the placement-tool as ordinarysingle ended cells. At the end, the most difficult task is for therouter-tool 1105, which matches the two output lines of each compoundgate. In one prototype, a Xilinx Virtex-II Development Kit by AvnetDesign Services is used in connection with the following software tools:DesignAnalyzer from Synopsys, ISE from Xilinx and ModelSim from MentorGraphics.

In an FPGA implementation of DPA-proof combinatorial logic, more thanone compound gate can be implemented in one slice. A restrictedcombination of several compound logic gates will result in a newcompound logic gate that mimics the behavior of a SABL gate. Thispractice will decrease the area and timing requirements.

One of ordinary skill in the art will recognize that the architecturesand methodologies described herein can be implemented using existingstandard cell libraries and existing software tools, and can beintegrated in a common automated design flow. Being able to apply themethodology on an FPGA opens the door to do secure prototyping of adesign on a single FPGA, or even to add an FPGA module on a Smart Card,which will extend the lifespan and increase the versatility of aparticular Smart Card product.

For CMOS logic, the power supply variations exploited by DPA depend onthe load capacitance that is charged and discharged during operation ofthe logic circuit. The load capacitance has four components: theinternal node capacitance; the intrinsic output capacitance; theinterconnect capacitance; and the intrinsic input capacitance of theload. In case of an ASIC with static complementary CMOS standard cells,the internal node capacitances are typically different, as are theintrinsic input and output capacitances. With shrinking channel-lengthof the transistors, however, the interconnect capacitance becomes thedominant capacitance. This makes it appropriate to concentrate on theinterconnect capacitances. Under the assumption that the differentialsignals travel in the same environment, the interconnect capacitancesare equivalent.

In case of an FPGA, it typically depends on the implementation of thelook-up table. For example, for the Virtex-II platform, the manufacturerstates in the datasheets that the propagation delay is independent ofthe function implemented. This implies that the internal and theintrinsic capacitances are more or less identical. For other FPGAplatforms this may or may not be the case. Here, it can be difficult toforce the router -tool to route the signals in the same environment. Thereason is that only a limited number of routing tracks may be available.

WDDL is not restricted to only AND and OR gates. For FPGA, differentcompound gates can be combined in one slice. A combination of a compoundgate also results in a secure compound gate. In other words, anycombination of non-inverting gates (e.g., AND and OR gates) and its dualwill behave as a WDDL gate. Therefore, a design can be synthesized withan extended library. This library contains all the AND, NAND, OR, NOR,AOI, OAI, XOR, MX, BUF, DLY, etc., of the original standard celllibrary.

A WDDL gate includes of a parallel combination of two positivecomplementary gates. A positive gate produces a zero output for anall-zero input. A complementary (or dual) gate computes the false outputof the original logic gate using the false inputs of the original gate.

Any combination of AND-, OR- operators and its dual, which isconstructed with the help of the De-Morgan's law (where the AND and ORoperators are interchanged and the input signals are inverted), willbehave as a WDDL gate. The resulting compound gate (1) is differentialas it is constructed to be; (2) propagates the precharge wave sincepositive operators are used; and (3) has an approximately 100% switchingfactor as it is a dual gate with AND and OR operators. AOI(AND-OR-INVERT), XOR, MUX, etc. can all be implemented.

FIG. 12A shows an example of a sample logic function 1200 with inputsA0, A1, B0, and a single-ended output Y. The inputs A0 and A1 areprovided to respective input of a two-input NAND gate 1201. An output ofthe NAND gate 1201 is provided to a first input of a NAND gate 1202. Theinput B0 is provided to a second input of the NAND gate 1201. An outputof the NAND gate 1202 is the output Y.

FIG. 12B shows one embodiment of a WDDL implementation 1210 of the logicfunction 1200 shown in FIG. 12A. In FIG. 12B, the inputs A0 and A1 areprovided to respective input of a two-input AND gate 1211. An output ofthe AND gate 1211 is provided to a first input of a NOR gate 1212. Theinput B0 is provided to a second input of the NOR gate 1212. An outputof the NOR gate 1212 is provided through an inverter 1215 as the outputY. The inverted inputs A0 and A1 are provided to respective inputs of atwo-input OR gate 1213. An output of the OR gate 1213 is provided to afirst input of a NAND gate 1214. The input B0 is provided to a secondinput of the NAND gate 1214. An output of the NAND gate 1214 is providedthrough an inverter 1216 as the inverted output Y.

A similar strategy can be used to implement the XOR and XNOR combinationwith only positive gates.

Differential pair and shielded routing has been available throughshape-based routers whose antecedents are in the PCB domain, whereelectrical constraints are historically more dominant. PCB routers havebeen adapted to IC routing and offer differential-pair or shieldedrouting options. However, router performance and completion rate degraderapidly with increasing number of such constraints. In one experiment,an attempt to use Cadence Chip Assembly Router version 11.0.06 to routea differential design required almost 8 hrs in time on a SUN ULTRA 5.The routing did not complete. In comparison, Cadence SiliconEnsemblewith the techniques described herein only required 3 CPU seconds toroute in one experiment.

In one embodiment, the differential pair is routed as a singlerepresenting wire. The differential design is routed with thatrepresenting wire and then the representing wire is decomposed into thedifferential wire. The representing wire is represented such that aftertransformation in the two differential wires no spacing errors orviolations occur. After place and route with the representing wire, theresulting design is transformed into the final differential design. Thetransformation includes two translations of the representing wire and awidth definition of each of the 2 differential wires.

The representing wires are routed using gates in which the output pinsand input pins represent the differential output pins and input pins ofthe differential gates. When the representing wires are split intodifferential pairs, the representing input and output pins of thedifferential logic standard cells are replaced by corresponding pairs ofpins whose locations in the standard cells correspond to thetransformation of the representing wire into the differential pairs.

In one embodiment, the differential pair is routed as a single “fat”wire 1301 as shown in FIG. 13 a. The differential design is routed withthe fat wire 1301 and then the fat wire 1301 is decomposed into thedifferential wires 1302, 1303 as shown in FIG. 13 b. The fat wire 1301is then omitted as shown in FIG. 13 c. In one embodiment, the line widthof the fat wire 1301 covers the space occupied by the two differentialwires 1302, 1303. The centerline of the fat wire 1301 is the centerlinebetween the two differential wires 1302, 1303. The width of the fat wireW_(f) is set by the summation of the pitch P_(n) of the normal wires andtwo times half the width of the normal wire W_(n): W_(f)=P_(n)+2W_(n)/2.The pitch, which is the distance between the centerline of two adjacentwires, P_(f) of the fat wires is set by the summation of 2 times halfthe width of the fat wire and the desirable distance Δ between the fatwires: P_(f)=2W_(f)/2+Δ. The distance Δ can be made relatively large toreduce cross-talk effects. The minimum spacing rules do not change.After place & route with the fat wire, the resulting design istransformed into the final differential design. The transformationincludes two translations of the fat wire and a width reduction to thenormal width. In one embodiment, the differential wires 1302, 1303 arethe same line width. In one embodiment, the differential wires 1302,1303 are different line widths.

Since the centerline between two normal wires is typically thecenterline of the fat wire 1301, a translation of the fat wire in thepositive direction will result in one differential line and a negativetranslation in the in the other line. The translation occurs both in thehorizontal and the vertical direction. FIGS. 13A-C show the fat wires(A), translation operation (B), and differential routes (C). As shown inFIGS. 13A-C, a consistent shift of all segments of the fat wire with aΔX in the X direction and a ΔY in the Y direction will result in onewire; a shift with a −ΔX and a −ΔY in the other wire. The shifts ΔX andΔY are half the pitch lengths of the normal wires in the X and Ydirection. Note that ΔX and ΔY can be negative. For example, in oneembodiment, ΔX is a negative offset and ΔY is a positive offset.

The resulting differential wires 1302, 1303 have the same number of viasand segments. Each segment has the same length in both wires and isrouted over the same number of wires in the other metal layers. As aresult, both lines have the same distributed resistances and parasiticcapacitances to the substrate and to the routes in the other metallayers.

As can be seen in FIGS. 13A-C, the vias are aligned on a positive tilteddiagonal. The input and output pins of the standard cells are also bealigned likewise and with the same offsets. The upper pin is the pinassociated with the true net, the lower with the false net. This allowsthe translation to be done in a consistent way. This also means that thestandard cells are placed in the RO direction, otherwise this rule isviolated. In one embodiment, allowing different cell orientationsprovides smaller wire length and smaller area, but the fat wiresplitting is more complicated.

In one embodiment, the fat wires are routed using gates in which theoutput pins and input pins are fat. When the fat wires are split intodifferential pairs, the fat input and output pins of the differentiallogic standard cells are replaced by corresponding pairs of pins whoselocations in the standard cells correspond to the transformation of thefat wire into the differential pairs. In some embodiments, it is notpossible to include the exact differential pin information in theabstract views of the fat gates. However, access direction to the fatpin can be limited by defining appropriate obstructions such that thewire split does not induce any violations.

If the fat wire 1301 takes a turn in one metal layer, the wires of adifferential route may cross in the same metal layer and result in anelectric short between both wires. This can not happen if each metallayer is only routed in a preferred direction, e.g., only in thevertical direction or only in the horizontal direction. In oneembodiment, allowing wrong way routing and turns in one layer providessmaller wire length and smaller area, but the fat wire splitting is morecomplicated.

In one embodiment, the differential pair is routed as a singlerepresenting wire. The representing wire is routed on a large grid thathas been defined such that there will be no spacing violations aftersplitting. Doubling the original grid pitches results in such a grid.After place & route with the representing wire, the resulting design istransformed into the final differential design. The transformationincludes two translations of the representing wire and a widthdefinition of each of the two differential wires.

In one embodiment, the grid and the standard cells are defined asfollows: (1) the horizontal and vertical pitches of the fat grid aredouble that of the normal grid; and (2) the normal and fat grids have anoffset of half their pitch length in both the horizontal and verticaldirection. With this definition: (1) the standard cell dimensions aremultiples of the horizontal and vertical pitch of the fat and the normalgrid; (2) the fat pins are situated on the crossings of the fat grid,the differential pins on the crossings of the normal one; and (3) thedifferential pins can obtained by shifting the fat pin with half a pitchlength of the normal grid in both the horizontal and vertical direction.

The methods above describe methodologies to route a design where allwires are differential. It is, however, possible to combine single-endedrouting and differential routing.

In one embodiment, the design can be routed in two stages as shown inFIG. 14. First the differential lines are routed, and subsequently witha new library database the single ended lines are routed, or vice versa.

In one embodiment, the differential and single-ended wires can be routedconcurrently by defining the fat routes or the single ended routes asnon-default routing rules. Or, one can route every wire as a fat wireand subsequently transform the single ended signals into a single lineand the differential signals into two lines

In one embodiment, routing is provided by Silicon Ensemble. The wires inthe routed ‘fat.def’ design file are described as lines between twopoints and vias are assigned as points. The wire width and viacharacteristics are defined in the .lef library database. As a result,the parser only needs to translate the (X,Y) coordinates of the endpoints without worrying about the wire characteristics. The translationis done by (1) repeating each statement that defines a net; (2)attaching the first statement to the positive pins and translating it ina positive (ΔX,ΔY) direction; and (3) attaching the second statement tothe negative pins and translate it in a negative (ΔX,ΔY) direction.Recall that ΔX and ΔY are half the pitch lengths of the normal wires inthe X and Y direction. Besides the translation of the nets, each fatgate in the ‘fat.def’ file is substituted by its correspondingdifferential gate. The transformation procedure includes: (1) parsingthe placed and routed fat design to reflect the differential design and(2) reading in the differential library database. The differential‘diff.lef’ library database contains the normal grid definition, normalwire definition, normal via definition and the differential gates withdifferential pin information.

Thus, multiple differential pairs can be routed with the aid of an EDAtool to the lines in parallel and in adjacent tracks such that they havethe same parasitic capacitances and resistances. Differential designsare routed with differential pairs almost a factor three faster thanwhen the same differential design is routed regularly without anyconstraints.

In one experiment, the variation between the capacitance at the truesignal net and the capacitance at the corresponding false signal net isup to a factor four for the regular (non-differential) route procedureprovided by Silicon Ensemble. By contrast, the differential pair routeprocedure shows negligible variation in capacitance between the twodifferential lines. The absolute values of the capacitances on the otherhand, are similar between the two routing procedures. The mean energyconsumption per clock cycle is 42.72 pJ and 44.21 pJ for the regularroute and the differential pair route respectively. The normalizedenergy deviation, which specifies the absolute range of the variation onthe energy consumption per cycle, is 1% for the regular route and 0.7%for the differential pair route. The normalized standard deviation is0.2% and 0.1% respectively.

The differential pair routing herein can be used as part of a securedigital design flow, supported by EDA tools from verilog/vhdl to layout.

Cross-talk, which is the phenomenon of noise induced on one wire by asignal switching on a neighboring wire, has an effect on the powerconsumption. Cross-talk effects are caused by the distributedcapacitance to relatively nearby wires (e.g., wires in the same orrelatively nearby metal layers). Routing the two output nets in parallelalready removes the uncertainty of one neighbor: during a switchingevent one output line switches, and the other output line remains quiet.Uncertainty can be reduced by shielding the differential routes oneither side with a VDD or VSS line. Reserving one grid line out of threeupfront for a power line reduces the problem to routing two differentiallines. Note that the approach of alternating signal lines and quietpower lines can produce predictable interconnect parasitic capacitivecouplings. Alternatively, the cross-talk effects can be controlled byincreasing the distance between different differential routes. In oneembodiment, an iterative design flow can be used to identify and correctmismatches, as shown in FIGS. 15A-15C.

FIG. 15A shows parasitic capacitive coupling 1503 between a differentialpair 1500 and a differential pair 1501. FIG. 15B shows that a groundconductor, power conductor, or other conductor 1504 placed between thepairs 1500 and 1501. FIG. 15C shows that the parasitic capacitivecoupling 1503 can be reduced by increasing the distance between thepairs 1500 and 1501.

Although the foregoing has been a description and illustration ofspecific embodiments of the invention, various modifications and changescan be made thereto by persons skilled in the art, without departingfrom the scope and spirit of the invention as defined by the claims.

1. A Wave Dynamic Differential Logic, comprising: a plurality ofdifferential logic cells arranged in a combinatorial logic tree and eachhaving inverted combinatorial data-bearing inputs and correspondingnon-inverted combinatorial data-bearing inputs, each of said pluralityof differential logic cells configured to provide one or more invertedlogic outputs and corresponding one or more non-inverted logic outputs,each of said plurality of differential logic cells configured to receivea precharge wave and/or a predischarge wave on said invertedcombinatorial data-bearing inputs and non-inverted combinatorialdata-bearing inputs of the respective differential logic cell and topropagate said precharge wave and/or said predischarge wave from saidinverted combinatorial data-bearing inputs and correspondingnon-inverting combinatorial data-bearing inputs of the respectivedifferential logic cell to said inverted logic outputs and saidnon-inverted logic outputs of the respective differential logic cell,wherein each of said plurality of differential logic cells is configuredto receive and propagate said precharge wave and/or said predischargewave during a precharge and/or pre-discharge phase, and is furtherconfigured to, during an evaluation phase, receive differential data onits inverted combinatorial data bearing inputs and its correspondingnon-inverted combinatorial data-bearing inputs and evaluate saiddifferential data to produce differential output data on its invertedlogic outputs and its non-inverted logic outputs, wherein said prechargewave and/or said predischarge wave is encoded in data received on theinverted and non-inverted combinatorial data-bearing inputs of each ofsaid plurality of differential logic cells, and wherein each of saidplurality of differential logic cells is precharged or predischargedwithout distributing a separate precharge or predischarge signal to theplurality of differential logic cells.
 2. The Wave Dynamic DifferentialLogic of claim 1, comprising positive logic.
 3. The Wave DynamicDifferential Logic of claim 1, wherein the combinatorial logic tree hasa relatively constant power consumption that does not depend on thecontent of the differential data.
 4. The Wave Dynamic Differential Logicof claim 3, wherein the combinatorial logic tree forms part of aDPA-resistant encryption module.
 5. A Wave Dynamic Differential Logic,comprising: a plurality of differential logic cells each having invertedcombinatorial data-bearing inputs and corresponding non-invertedcombinatorial data-bearing inputs, each of said plurality ofdifferential logic cells configured to provide one or more invertedlogic outputs and corresponding one or more non-inverted logic outputs;and a pre-discharged logic cell configured to receive a pre-dischargesignal and, in response to said pre-discharge signal, to generate apre-discharge wave to pre-discharge and propagate through each of saidplurality of differential logic cells from said inverted combinatorialdata-bearing inputs and non-inverted combinatorial data-bearing inputsof the respective differential logic cell to said inverted logic outputsand non-inverted logic outputs of the respective differential logic celland/or a precharged logic cell configured to receive a precharge signaland, in response to said precharge signal, to generate a precharge waveto pre-charge and propagate through each of said plurality ofdifferential logic cells from said inverted combinatorial data-bearinginputs and non-inverted combinatorial data-bearing inputs of therespective differential logic cell to said inverted logic outputs andnon-inverted logic outputs of the respective differential logic cell,wherein said precharge wave and/or said predischarge wave is encoded indata received on the inverted and non-inverted combinatorialdata-bearing inputs of each of the plurality of differential logiccells, and wherein each of said plurality of differential logic cells ispredischarged or precharged without distributing a separate predischargeor precharge signal to the plurality of differential logic cells.
 6. TheWave Dynamic Differential Logic of claim 5, comprising positive logic.7. A Wave Dynamic Differential Logic, comprising: a plurality ofdifferential logic cells arranged in a combinatorial logic tree and eachhaving inverted combinatorial data-bearing inputs and correspondingnon-inverted combinatorial data-bearing inputs, each of said pluralityof differential logic cells configured to provide one or more invertedlogic outputs and corresponding one or more non-inverted logic outputs;and a precharge operator comprising first and second outputs andconfigured to receive a precharge signal and differential datacomprising inverted differential data and corresponding non-inverteddifferential data, the precharge operator configured, during anevaluation phase, to provide the inverted differential data on the firstoutput and the non-inverted differential data on the second output, and,during a precharge phase, to provide the precharge signal on the firstand second outputs; a differential logic register comprising a firstoutput and a second output and configured to: during the prechargephase, to receive a precharge signal and, in response to said prechargesignal, to generate a pre-charge wave and provide the pre-charge wave tothe combinatorial logic tree on the first second outputs to pre-chargeand propagate through each of said plurality of differential logic cellsfrom said inverted inputs and non-inverted inputs of the respectivedifferential logic cell to said inverted logic outputs and non-invertedlogic outputs of the respective differential logic cell; and during theevaluation phase, to provide the differential data to the combinatoriallogic tree on the first and second outputs; and wherein said prechargewave is encoded in data received on the inverted and non-invertedcombinatorial data-bearing inputs of each of the plurality ofdifferential logic cells and each of said plurality of differentiallogic cells is precharged without distributing a separate prechargesignal to any of the plurality of differential logic cells.
 8. The WaveDynamic Differential Logic of claim 7, comprising positive logic.
 9. TheWave Dynamic Differential Logic of claim 7, wherein the Wave DynamicDifferential Logic has a relatively constant power consumption that doesnot depend on the differential data.
 10. The Wave Dynamic DifferentialLogic of claim 9, wherein the Wave Dynamic Differential Logic forms partof a DPA-resistant encryption module.
 11. A Wave Dynamic DifferentialLogic, comprising: a plurality of differential logic cells arranged in acombinatorial logic tree and each having combinatorial data-bearinginverted inputs and corresponding non-inverted combinatorialdata-bearing inputs, each of said plurality of differential logic cellsconfigured to provide one or more inverted logic outputs andcorresponding one or more non-inverted logic outputs; and a predischargeoperator comprising first and second outputs, and configured to receivea predischarge signal and differential data comprising inverteddifferential data and corresponding non-inverted differential data, thepredischarge operator configured, during an evaluation phase, to providethe inverted differential data on the first output and the non-inverteddifferential data on the second output, and, during a predischargephase, to provide the predischarge signal on the first and secondoutputs; a differential logic register comprising first a second outputsand configured to: during the predischarge phase, to receive apre-discharge signal and, in response to said pre-discharge signal, togenerate a pre-discharge wave and provide the predischarge wave to thecombinatorial logic tree on the first and second outputs topre-discharge and propagate through each of said differential logiccells from said inverted inputs and non-inverted inputs of therespective differential logic cell to said inverted logic outputs andnon-inverted logic outputs of the respective differential logic cell;and during the evaluation phase, to provide the differential data to thecombinatorial logic tree on the first and second outputs; and whereinsaid predischarge wave is encoded in data received on the inverted andnon-inverted combinatorial data-bearing inputs of each of the pluralityof differential logic cells and each of said plurality of differentiallogic cells is predischarged without distributing a separatepredischarge signal to the plurality of differential logic cells. 12.The Wave Dynamic Differential Logic of claim 11, comprising positivelogic.
 13. The Wave Dynamic Differential Logic of claim 11, wherein theWave Dynamic Differential Logic has a relatively constant powerconsumption that does not depend on the differential data.
 14. The WaveDynamic Differential Logic of claim 13, wherein the Wave DynamicDifferential Logic forms part of a DPA-resistant encryption module. 15.A Divided Wave Dynamic Differential Logic DPA-resistant logic circuit,comprising: a first single-ended logic tree comprising a plurality offirst combinatorial data-bearing logic tree inputs and a plurality offirst logic tree outputs and configured to, during an evaluation phase,receive inverted input data and corresponding non-inverted input data onsaid first combinatorial data-bearing logic tree inputs and to producefirst output data on said first logic tree outputs, the first logic treecomprising a first plurality of logic gates; and a single-ended dual ofsaid first single-ended logic tree connected in parallel with the firstsingle-ended logic tree and comprising a plurality of dual combinatorialdata-bearing logic tree inputs and a plurality of dual logic treeoutputs and configured to, during said evaluation phase, receive saidinverted input data and said corresponding non-inverted input data onsaid dual combinatorial data-bearing logic tree inputs and produceinverted first output data on said dual logic tree outputs, the dual ofsaid first logic tree comprising a second plurality of logic gates, thefirst output data comprising single-ended non-inverted output data andthe inverted first output data comprising single-ended correspondinginverted output data, said first logic tree and said dual of said firstlogic tree further configured to, during a precharge and/orpre-discharge phase, receive a precharge wave and/or a pre-dischargewave on said first combinatorial data-bearing logic tree inputs and saiddual combinatorial data-bearing logic tree inputs and propagate saidprecharge wave and/or pre-discharge wave through each of the firstplurality of logic gates and each of the second plurality of logic gatesto said first logic tree outputs and said dual logic tree outputs,wherein said precharge wave is encoded in data received on thecombinatorial data-bearing logic tree inputs of the first logic tree andthe dual combinatorial data-bearing logic tree inputs of the secondlogic tree, and wherein each of said first plurality of logic gates andeach of said second plurality of logic gates is precharged orpre-discharged without distributing a separate precharge orpre-discharge signal to the first plurality of logic gates or to thesecond plurality of differential logic gates.
 16. The Wave DynamicDifferential Logic of claim 15, wherein the logic circuit has arelatively constant power consumption that does not depend on thedifferential data.
 17. The Wave Dynamic Differential Logic of claim 15,wherein the single-ended dual is derived from the first single-endedlogic tree.
 18. The Wave Dynamic Differential Logic of claim 17, whereinthe first plurality of logic gates of the first single-ended logic treecomprise one or more AND gates and one or more OR gates, and wherein thesecond plurality of logic gates of the single-ended dual comprise: oneor more OR gates corresponding to each of the one or more AND gates ofthe first plurality of logic gates; and one or more AND gatescorresponding to each of the one or more OR gates of the first pluralityof logic gates.
 19. A Wave Dynamic Differential Logic, comprising: aplurality of differential logic cells each having inverted combinatorialdata-bearing inputs and corresponding non-inverted combinatorialdata-bearing inputs, each of said differential logic cells configured toprovide one or more inverted logic outputs and corresponding one or morenon-inverted logic outputs; and a master-slave differential dynamiclogic register configured to receive a pre-charge wave and to transmiton the pre-charge wave to pre-charge each of said plurality ofdifferential logic cells, each of the plurality of differential logiccells further configured to receive the precharge wave on said invertedcombinatorial data-bearing inputs and non-inverted combinatorialdata-bearing inputs of the respective differential logic cell and topropagate said pre-charge wave from said inverted combinatorialdata-bearing inputs and corresponding non-inverted combinatorialdata-bearing inputs of the respective differential logic cell to saidinverted logic outputs and said non-inverted logic outputs of therespective differential logic cell, wherein said precharge wave isencoded in data received on the inverted and non-inverted combinatorialdata-bearing inputs of each of the plurality of differential logiccells, and wherein each of said plurality of differential logic cells ispre-charged without distributing a separate pre-charge signal to theplurality of differential logic cells.
 20. A Wave Dynamic DifferentialLogic, comprising: a plurality of differential logic cells each havinginverted combinatorial data-bearing inputs and correspondingnon-inverted combinatorial data-bearing inputs, each of said pluralityof differential logic cells configured to provide one or more invertedlogic outputs and corresponding one or more non-inverted logic outputs;and a differential dynamic logic register configured to receive apre-charge signal and, in response to said pre-charge signal, togenerate a pre-charge wave to pre-charge each of said plurality ofdifferential logic cells, each of said plurality of differential logiccells further configured to receive the precharge wave on said invertedcombinatorial data-bearing inputs and non-inverted combinatorialdata-bearing inputs of the respective differential logic cell and topropagate said pre-charge wave from said inverted combinatorialdata-bearing inputs and corresponding non-inverting combinatorialdata-bearing inputs of the respective differential logic cell to saidinverted logic outputs and said non-inverted logic outputs of therespective differential logic cell, wherein said precharge wave isencoded in data received on the inverted and non-inverted combinatorialdata-bearing inputs of each of the plurality of differential logiccells, and wherein each of said plurality of differential logic cells ispre-charged without distributing a separate pre-charge signal to theplurality of differential logic cells.
 21. A Wave Dynamic DifferentialLogic, comprising: a plurality of differential logic cells each havinginverted combinatorial data-bearing inputs and correspondingnon-inverted combinatorial data-bearing inputs, each of saiddifferential logic cells configured to provide one or more invertedcombinatorial data-bearing logic outputs and corresponding one or morenon-inverted combinatorial data-bearing logic outputs; and amaster-slave differential dynamic logic register configured to receive apre-discharge wave and to transmit on the pre-discharge wave topre-discharge each of said plurality of differential logic cells, eachof the plurality of differential logic cells further configured toreceive the pre-discharge wave on said inverted combinatorialdata-bearing inputs and non-inverted combinatorial data-bearing inputsof the respective differential logic cell and to propagate saidpre-discharge wave from said inverted combinatorial data-bearing inputsand corresponding non-inverting combinatorial data-bearing inputs of therespective differential logic cell to said inverted logic outputs andsaid non-inverted logic outputs of the respective differential logiccell, wherein said pre-discharge wave is encoded in data received on theinverted and non-inverted combinatorial data-bearing inputs of each ofthe plurality of differential logic cells, and wherein each of saidplurality of differential logic cells is pre-discharged withoutdistributing a separate pre-discharge signal to the plurality ofdifferential logic cells.
 22. A Wave Dynamic Differential Logic,comprising: a plurality of differential logic cells each having invertedcombinatorial data-bearing inputs and corresponding non-invertedcombinatorial data-bearing inputs, each of said differential logic cellsconfigured to provide one or more inverted logic outputs andcorresponding one or more non-inverted logic outputs; and a differentialdynamic logic register configured to receive a pre-discharge signal andgenerate a pre-discharge wave to pre-discharge each of said plurality ofdifferential logic cells, each of the plurality of differential logiccells further configured to receive the pre-discharge wave on saidinverted combinatorial data-bearing inputs and non-invertedcombinatorial data-bearing inputs of the respective differential logiccell and to propagate said pre-discharge wave from said invertedcombinatorial data-bearing inputs and corresponding non-invertingcombinatorial data-bearing inputs of the respective differential logiccell to said inverted logic outputs and said non-inverted logic outputsof the respective differential logic cell, wherein said pre-dischargewave is encoded in data received on the inverted and non-invertedcombinatorial data-bearing inputs of each of the plurality ofdifferential logic cells, and wherein each of said plurality ofdifferential logic cells is pre-discharged without distributing aseparate pre-discharge signal to the plurality of differential logiccells.